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        <h1 id="机器学习之DBSCAN算法"><a href="#机器学习之DBSCAN算法" class="headerlink" title="机器学习之DBSCAN算法"></a>机器学习之DBSCAN算法</h1><p>上一篇将了kmeans，这一篇将dbscan</p>
<h2 id="监督算法DBSCAN"><a href="#监督算法DBSCAN" class="headerlink" title="监督算法DBSCAN"></a>监督算法DBSCAN</h2><p>DBSCAN(Density-Based Spatial Clustering of Applications with Noise)</p>
<p>相对于kmeans，dbscan不需要指定簇的个数</p>
<h3 id="基本概念"><a href="#基本概念" class="headerlink" title="基本概念"></a>基本概念</h3><ol>
<li>核心对象<br> 若某个点的密度达到算法设定的阈值则其为核心点（即r领域内点的数量不小于minPts）</li>
<li>领域的距离阈值：设定的半径r</li>
<li>直接密度可达<br> 若某点p在点q的r领域内，且q是核心点则p-q直接密度可达</li>
<li>密度可达<br> 若有一个点的序列q0、q1、…qk，对任意qi-qi-1是直接密度可达的，则称从q0到qk密度可达，这实际上是直接密度可达的“传播”</li>
<li>密度相连<br> 若从某核心点p出发，点q和点k都是密度可达的，则称点q和点k是密度相连的</li>
<li>边界点<br> 属于某一个类的非核心点，不能发展下线了</li>
<li>噪声点<br> 不属于任何一个簇的点，从任何一个核心点出发都是密度不可达的</li>
</ol>
<h3 id="dbscan处理流程"><a href="#dbscan处理流程" class="headerlink" title="dbscan处理流程"></a>dbscan处理流程</h3><p>通俗的将讲，dbscan算法就是找到一个点就开始画圈，在圈内的就是同一个类别，同时再以圈内的其他点作为圆心继续画圈，最后得到的这些点就是一个簇了</p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line">标记所有对象为unvisited</span><br><span class="line">do</span><br><span class="line">随机选择一个unvisited对象p</span><br><span class="line">标记p为visited</span><br><span class="line">if p的r领域内至少有MinPts个对象</span><br><span class="line">    创建一个新簇C，并把p添加到C</span><br><span class="line">    令N为p的r领域中的对象集合</span><br><span class="line">    for N中每个点p</span><br><span class="line">        if p 是unvisited</span><br><span class="line">            标记p 为visited</span><br><span class="line">            if p 的r领域至少有MinPts个对象，把这些对象添加到N</span><br><span class="line">            如果p还不是任何簇的成员，把p 添加到C</span><br><span class="line">    end for</span><br><span class="line">    输出C</span><br><span class="line">else</span><br><span class="line">    标记 p 为噪声点</span><br><span class="line">until 没有标记为unvisited的对象</span><br></pre></td></tr></table></figure>
<h3 id="参数选择"><a href="#参数选择" class="headerlink" title="参数选择"></a>参数选择</h3><p>dbscan需要设定半径r与MinPts</p>
<ol>
<li><p>对于半径r<br> 一般方式是找突变点，选择一个点，计算该点到其他点的距离，从小到大排序，找距离变化最大的边界</p>
</li>
<li><p>MinPts<br> 一般取小一些，然后多次尝试</p>
</li>
</ol>
<h3 id="优缺点"><a href="#优缺点" class="headerlink" title="优缺点"></a>优缺点</h3><p><strong>优点</strong></p>
<ol>
<li>不需要指定簇的个数</li>
<li>可以发现任意形状的簇</li>
<li>擅长找到离群点（检测任务）</li>
<li>两个参数就够了</li>
</ol>
<p><strong>缺点</strong></p>
<ol>
<li>高纬度有些困难（可以做降维）</li>
<li>参数难以选择（参数对结果的影响非常大）</li>
<li>Sklearn中效率很慢（数据消减策略）</li>
<li>数据太大可能发生内存溢出</li>
</ol>
<h3 id="可视化展示"><a href="#可视化展示" class="headerlink" title="可视化展示"></a>可视化展示</h3><p><a href="https://www.naftaliharris.com/blog/visualizing-k-means-clustering/">Visualizing K-Means Clustering</a> 是一个国外的网友做的一个可视化网站</p>
<h2 id="使用sklearn进行DBSCAN聚类"><a href="#使用sklearn进行DBSCAN聚类" class="headerlink" title="使用sklearn进行DBSCAN聚类"></a>使用sklearn进行DBSCAN聚类</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">&gt;&gt;&gt; </span><span class="keyword">from</span> sklearn.cluster <span class="keyword">import</span> DBSCAN</span><br><span class="line"><span class="meta">&gt;&gt;&gt; </span><span class="keyword">import</span> pandas <span class="keyword">as</span> pd</span><br><span class="line"><span class="meta">&gt;&gt;&gt; </span>beer = pd.read_csv(<span class="string">'data.txt'</span>, sep=<span class="string">' '</span>)</span><br><span class="line"><span class="meta">&gt;&gt;&gt; </span>X = beer[[<span class="string">"calories"</span>, <span class="string">"sodium"</span>, <span class="string">"alcohol"</span>, <span class="string">"cost"</span>]]</span><br><span class="line"><span class="meta">&gt;&gt;&gt; </span>db = DBSCAN(eps=<span class="number">10</span>, min_samples=<span class="number">2</span>).fit(X)</span><br><span class="line"><span class="meta">&gt;&gt;&gt; </span>labels = db.labels_</span><br><span class="line"><span class="meta">&gt;&gt;&gt; </span>beer[<span class="string">'cluster_db'</span>] = labels</span><br><span class="line"><span class="meta">&gt;&gt;&gt; </span>beer.sort_values(<span class="string">'cluster_db'</span>)</span><br><span class="line">                    name  calories  sodium  alcohol  cost  cluster_db</span><br><span class="line"><span class="number">9</span>        Budweiser_Light       <span class="number">113</span>       <span class="number">8</span>      <span class="number">3.7</span>  <span class="number">0.40</span>          <span class="number">-1</span></span><br><span class="line"><span class="number">3</span>            Kronenbourg       <span class="number">170</span>       <span class="number">7</span>      <span class="number">5.2</span>  <span class="number">0.73</span>          <span class="number">-1</span></span><br><span class="line"><span class="number">6</span>             Augsberger       <span class="number">175</span>      <span class="number">24</span>      <span class="number">5.5</span>  <span class="number">0.40</span>          <span class="number">-1</span></span><br><span class="line"><span class="number">17</span>   Heilemans_Old_Style       <span class="number">144</span>      <span class="number">24</span>      <span class="number">4.9</span>  <span class="number">0.43</span>           <span class="number">0</span></span><br><span class="line"><span class="number">16</span>                 Hamms       <span class="number">139</span>      <span class="number">19</span>      <span class="number">4.4</span>  <span class="number">0.43</span>           <span class="number">0</span></span><br><span class="line"><span class="number">14</span>                 Kirin       <span class="number">149</span>       <span class="number">6</span>      <span class="number">5.0</span>  <span class="number">0.79</span>           <span class="number">0</span></span><br><span class="line"><span class="number">13</span>                 Becks       <span class="number">150</span>      <span class="number">19</span>      <span class="number">4.7</span>  <span class="number">0.76</span>           <span class="number">0</span></span><br><span class="line"><span class="number">12</span>        Michelob_Light       <span class="number">135</span>      <span class="number">11</span>      <span class="number">4.2</span>  <span class="number">0.50</span>           <span class="number">0</span></span><br><span class="line"><span class="number">10</span>                 Coors       <span class="number">140</span>      <span class="number">18</span>      <span class="number">4.6</span>  <span class="number">0.44</span>           <span class="number">0</span></span><br><span class="line"><span class="number">0</span>              Budweiser       <span class="number">144</span>      <span class="number">15</span>      <span class="number">4.7</span>  <span class="number">0.43</span>           <span class="number">0</span></span><br><span class="line"><span class="number">7</span>   Srohs_Bohemian_Style       <span class="number">149</span>      <span class="number">27</span>      <span class="number">4.7</span>  <span class="number">0.42</span>           <span class="number">0</span></span><br><span class="line"><span class="number">5</span>          Old_Milwaukee       <span class="number">145</span>      <span class="number">23</span>      <span class="number">4.6</span>  <span class="number">0.28</span>           <span class="number">0</span></span><br><span class="line"><span class="number">4</span>               Heineken       <span class="number">152</span>      <span class="number">11</span>      <span class="number">5.0</span>  <span class="number">0.77</span>           <span class="number">0</span></span><br><span class="line"><span class="number">2</span>              Lowenbrau       <span class="number">157</span>      <span class="number">15</span>      <span class="number">0.9</span>  <span class="number">0.48</span>           <span class="number">0</span></span><br><span class="line"><span class="number">1</span>                Schlitz       <span class="number">151</span>      <span class="number">19</span>      <span class="number">4.9</span>  <span class="number">0.43</span>           <span class="number">0</span></span><br><span class="line"><span class="number">8</span>            Miller_Lite        <span class="number">99</span>      <span class="number">10</span>      <span class="number">4.3</span>  <span class="number">0.43</span>           <span class="number">1</span></span><br><span class="line"><span class="number">11</span>           Coors_Light       <span class="number">102</span>      <span class="number">15</span>      <span class="number">4.1</span>  <span class="number">0.46</span>           <span class="number">1</span></span><br><span class="line"><span class="number">19</span>         Schlitz_Light        <span class="number">97</span>       <span class="number">7</span>      <span class="number">4.2</span>  <span class="number">0.47</span>           <span class="number">1</span></span><br><span class="line"><span class="number">15</span>     Pabst_Extra_Light        <span class="number">68</span>      <span class="number">15</span>      <span class="number">2.3</span>  <span class="number">0.38</span>           <span class="number">2</span></span><br><span class="line"><span class="number">18</span>   Olympia_Goled_Light        <span class="number">72</span>       <span class="number">6</span>      <span class="number">2.9</span>  <span class="number">0.46</span>           <span class="number">2</span></span><br></pre></td></tr></table></figure>
      
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